# Copyright (c) [2024] []
#
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in all
# copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
# SOFTWARE.
import warnings
from sys import getsizeof
from timeit import default_timer as timer
# use numpy number of threads one
try:
from threadpoolctl import threadpool_info, threadpool_limits
user_api = threadpool_info()["user_api"]
threadpool_limits(limits=1, user_api=user_api)
except:
print("Warning: threadpoolctl could not make numpy use single thread!")
import numpy as np
import sisl
from mpi4py import MPI
try:
from tqdm import tqdm
tqdm_imported = True
except:
print("Please install tqdm for nice progress bar.")
tqdm_imported = False
from grogupy import *
[docs]
def main():
# runtime information
times = dict()
times["start_time"] = timer()
# input output stuff
######################################################################
######################################################################
######################################################################
infile = "/Users/danielpozsar/Downloads/nojij/Fe3GeTe2/monolayer/soc/lat3_791/Fe3GeTe2.fdf"
outfile = "./Fe3GeTe2_notebook"
magnetic_entities = [
dict(atom=3, l=2),
dict(atom=4, l=2),
dict(atom=5, l=2),
]
pairs = [
dict(ai=0, aj=1, Ruc=np.array([0, 0, 0])),
dict(ai=0, aj=2, Ruc=np.array([0, 0, 0])),
dict(ai=1, aj=2, Ruc=np.array([0, 0, 0])),
dict(ai=0, aj=2, Ruc=np.array([-1, -1, 0])),
dict(ai=1, aj=2, Ruc=np.array([-1, -1, 0])),
dict(ai=0, aj=2, Ruc=np.array([-1, 0, 0])),
dict(ai=1, aj=2, Ruc=np.array([-1, 0, 0])),
dict(ai=1, aj=2, Ruc=np.array([-2, 0, 0])),
dict(ai=1, aj=2, Ruc=np.array([-3, 0, 0])),
]
simulation_parameters = default_args
simulation_parameters["infile"] = infile
simulation_parameters["outfile"] = outfile
simulation_parameters["kset"] = 20
simulation_parameters["kdirs"] = "xy"
simulation_parameters["eset"] = 600
simulation_parameters["esetp"] = 10000
######################################################################
######################################################################
######################################################################
# MPI parameters
comm = MPI.COMM_WORLD
size = comm.Get_size()
rank = comm.Get_rank()
root_node = 0
if rank == root_node:
# include parallel size in simulation parameters
simulation_parameters["parallel_size"] = size
# check versions for debugging
try:
print("sisl version: ", sisl.__version__)
except:
print("sisl version unknown.")
try:
print("numpy version: ", np.__version__)
except:
print("numpy version unknown.")
# rename outfile
if not simulation_parameters["outfile"].endswith(".pickle"):
simulation_parameters["outfile"] += ".pickle"
# if ebot is not given put it 0.1 eV under the smallest energy
if simulation_parameters["ebot"] is None:
try:
eigfile = simulation_parameters["infile"][:-3] + "EIG"
simulation_parameters["ebot"] = read_siesta_emin(eigfile) - 0.1
simulation_parameters["automatic_ebot"] = True
except:
print("Could not determine ebot.")
print("Parameter was not given and .EIG file was not found.")
else:
simulation_parameters["automatic_ebot"] = False
# read sile
fdf = sisl.get_sile(simulation_parameters["infile"])
# read in hamiltonian
dh = fdf.read_hamiltonian()
# read unit cell vectors
simulation_parameters["cell"] = fdf.read_geometry().cell
# unit cell index
uc_in_sc_idx = dh.lattice.sc_index([0, 0, 0])
if rank == root_node:
print("\n\n\n\n\n")
print(
"#################################################################### JOB INFORMATION ###########################################################################"
)
print_job_description(simulation_parameters)
print(
"################################################################################################################################################################"
)
print("\n\n\n\n\n")
times["setup_time"] = timer()
print(f"Setup done. Elapsed time: {times['setup_time']} s")
print(
"================================================================================================================================================================"
)
NO = dh.no # shorthand for number of orbitals in the unit cell
# reformat Hamltonian and Overlap matrix for manipulations
hh, ss = build_hh_ss(dh)
# symmetrizing Hamiltonian and Overlap matrix to make them hermitian
for i in range(dh.lattice.sc_off.shape[0]):
j = dh.lattice.sc_index(-dh.lattice.sc_off[i])
h1, h1d = hh[i], hh[j]
hh[i], hh[j] = (h1 + h1d.T.conj()) / 2, (h1d + h1.T.conj()) / 2
s1, s1d = ss[i], ss[j]
ss[i], ss[j] = (s1 + s1d.T.conj()) / 2, (s1d + s1.T.conj()) / 2
# identifying TRS and TRB parts of the Hamiltonian
TAUY = np.kron(np.eye(NO), tau_y)
hTR = np.array([TAUY @ hh[i].conj() @ TAUY for i in range(dh.lattice.nsc.prod())])
hTRS = (hh + hTR) / 2
hTRB = (hh - hTR) / 2
# extracting the exchange field
traced = [spin_tracer(hTRB[i]) for i in range(dh.lattice.nsc.prod())] # equation 77
XCF = np.array(
[
np.array([f["x"] / 2 for f in traced]),
np.array([f["y"] / 2 for f in traced]),
np.array([f["z"] / 2 for f in traced]),
]
)
# check if exchange field has scalar part
max_xcfs = abs(np.array(np.array([f["c"] / 2 for f in traced]))).max()
if max_xcfs > 1e-12:
warnings.warn(
f"Exchange field has non negligible scalar part. Largest value is {max_xcfs}"
)
if rank == root_node:
times["H_and_XCF_time"] = timer()
print(
f"Hamiltonian and exchange field rotated. Elapsed time: {times['H_and_XCF_time']} s"
)
print(
"================================================================================================================================================================"
)
# initialize pairs and magnetic entities based on input information
pairs, magnetic_entities = setup_pairs_and_magnetic_entities(
magnetic_entities, pairs, dh, simulation_parameters
)
if rank == root_node:
times["site_and_pair_dictionaries_time"] = timer()
print(
f"Site and pair dictionaries created. Elapsed time: {times['site_and_pair_dictionaries_time']} s"
)
print(
"================================================================================================================================================================"
)
# generate k space sampling
kset = make_kset(
dirs=simulation_parameters["kdirs"], NUMK=simulation_parameters["kset"]
)
# generate weights for k points
wkset = np.ones(len(kset)) / len(kset)
# split the k points based on MPI size
kpcs = np.array_split(kset, size)
# use progress bar if available
if rank == root_node and tqdm_imported:
kpcs[root_node] = tqdm(kpcs[root_node], desc="k loop")
if rank == root_node:
times["k_set_time"] = timer()
print(f"k set created. Elapsed time: {times['k_set_time']} s")
print(
"================================================================================================================================================================"
)
# this will contain the three Hamiltonian in the
# reference directions needed to calculate the energy
# variations upon rotation
hamiltonians = []
# iterate over the reference directions (quantization axes)
for i, orient in enumerate(simulation_parameters["ref_xcf_orientations"]):
# obtain rotated exchange field and Hamiltonian
R = RotMa2b(simulation_parameters["scf_xcf_orientation"], orient["o"])
rot_XCF = np.einsum("ij,jklm->iklm", R, XCF)
rot_H_XCF = sum(
[np.kron(rot_XCF[i], tau) for i, tau in enumerate([tau_x, tau_y, tau_z])]
)
rot_H_XCF_uc = rot_H_XCF[uc_in_sc_idx]
# obtain total Hamiltonian with the rotated exchange field
rot_H = hTRS + rot_H_XCF # equation 76
# store the relevant information of the Hamiltonian
hamiltonians.append(dict(orient=orient["o"], H=rot_H))
# these are the rotations (for now) perpendicular to the quantization axis
for u in orient["vw"]:
# section 2.H
Tu = np.kron(np.eye(NO, dtype=int), tau_u(u))
Vu1, Vu2 = calc_Vu(rot_H_XCF_uc, Tu)
for mag_ent in magnetic_entities:
idx = mag_ent["spin_box_indices"]
# fill up the perturbed potentials (for now) based on the on-site projections
mag_ent["Vu1"][i].append(onsite_projection(Vu1, idx, idx))
mag_ent["Vu2"][i].append(onsite_projection(Vu2, idx, idx))
if rank == root_node:
times["reference_rotations_time"] = timer()
print(
f"Rotations done perpendicular to quantization axis. Elapsed time: {times['reference_rotations_time']} s"
)
print(
"================================================================================================================================================================"
)
# provide helpful information to estimate the runtime and memory
# requirements of the Greens function calculations
if rank == root_node:
print("Starting matrix inversions.")
if simulation_parameters["padawan_mode"]:
print("Padawan mode: ")
print(f"Total number of k points: {kset.shape[0]}")
print(
f"Number of energy samples per k point: {simulation_parameters['eset']}"
)
print(f"Total number of directions: {len(hamiltonians)}")
print(
f"Total number of matrix inversions: {kset.shape[0] * len(hamiltonians) * simulation_parameters['eset']}"
)
print(
f"The shape of the Hamiltonian and the Greens function is {NO}x{NO}={NO*NO}"
)
# https://stackoverflow.com/questions/70746660/how-to-predict-memory-requirement-for-np-linalg-inv
# memory is O(64 n**2) for complex matrices
memory_size = getsizeof(hamiltonians[0]["H"].base) / 1024
print(
f"Memory taken by a single Hamiltonian is: {getsizeof(hamiltonians[0]['H'].base) / 1024} KB"
)
print(f"Expected memory usage per matrix inversion: {memory_size * 32} KB")
print(
f"Expected memory usage per k point for parallel inversion: {memory_size * len(hamiltonians) * simulation_parameters['eset'] * 32} KB"
)
print(
f"Expected memory usage on root node: {len(np.array_split(kset, size)[0]) * memory_size * len(hamiltonians) * simulation_parameters['eset'] * 32 / 1024} MB"
)
print(
"================================================================================================================================================================"
)
# MPI barrier
comm.Barrier()
# make energy contour
cont = make_contour(
emin=simulation_parameters["ebot"],
enum=simulation_parameters["eset"],
p=simulation_parameters["esetp"],
)
eran = cont.ze
# sampling the integrand on the contour and the BZ
for k in kpcs[rank]:
# weight of k point in BZ integral
wk = wkset[rank]
# iterate over reference directions
for i, hamiltonian_orientation in enumerate(hamiltonians):
# calculate Hamiltonian and Overlap matrix in a given k point
H = hamiltonian_orientation["H"]
HK, SK = hsk(H, ss, dh.sc_off, k)
if simulation_parameters["parallel_solver_for_Gk"]:
Gk = parallel_Gk(HK, SK, eran, simulation_parameters["eset"])
else:
# solve Greens function sequentially for the energies, because of memory bound
Gk = sequential_GK(HK, SK, eran, simulation_parameters["eset"])
# store the Greens function slice of the magnetic entities
for mag_ent in magnetic_entities:
idx = mag_ent["spin_box_indices"]
mag_ent["Gii_tmp"][i] += onsite_projection(Gk, idx, idx) * wk
for pair in pairs:
# add phase shift based on the cell difference
phase = np.exp(1j * 2 * np.pi * k @ pair["Ruc"].T)
# get the pair orbital sizes from the magnetic entities
ai = magnetic_entities[pair["ai"]]["spin_box_indices"]
aj = magnetic_entities[pair["aj"]]["spin_box_indices"]
# store the Greens function slice of the magnetic entities
pair["Gij_tmp"][i] += onsite_projection(Gk, ai, aj) * phase * wk
pair["Gji_tmp"][i] += onsite_projection(Gk, aj, ai) / phase * wk
# summ reduce partial results of mpi nodes
for i in range(len(hamiltonians)):
for mag_ent in magnetic_entities:
comm.Reduce(mag_ent["Gii_tmp"][i], mag_ent["Gii"][i], root=root_node)
for pair in pairs:
comm.Reduce(pair["Gij_tmp"][i], pair["Gij"][i], root=root_node)
comm.Reduce(pair["Gji_tmp"][i], pair["Gji"][i], root=root_node)
if rank == root_node:
times["green_function_inversion_time"] = timer()
print(
f"Calculated Greens functions. Elapsed time: {times['green_function_inversion_time']} s"
)
print(
"================================================================================================================================================================"
)
if rank == root_node:
# iterate over the magnetic entities
for tracker, mag_ent in enumerate(magnetic_entities):
# iterate over the quantization axes
for i, Gii in enumerate(mag_ent["Gii"]):
storage = []
# iterate over the first and second order local perturbations
for Vu1, Vu2 in zip(mag_ent["Vu1"][i], mag_ent["Vu2"][i]):
# The Szunyogh-Lichtenstein formula
traced = np.trace(
(Vu2 @ Gii + 0.5 * Gii @ Vu1 @ Gii), axis1=1, axis2=2
) # this is the on site projection
# evaluation of the contour integral
storage.append(int_de_ke(traced, cont.we))
# fill up the magnetic entities dictionary with the energies
magnetic_entities[tracker]["energies"].append(storage)
# convert to np array
magnetic_entities[tracker]["energies"] = np.array(
magnetic_entities[tracker]["energies"]
)
# iterate over the pairs
for tracker, pair in enumerate(pairs):
# iterate over the quantization axes
for i, (Gij, Gji) in enumerate(zip(pair["Gij"], pair["Gji"])):
site_i = magnetic_entities[pair["ai"]]
site_j = magnetic_entities[pair["aj"]]
storage = []
# iterate over the first order local perturbations in all possible orientations for the two sites
for Vui in site_i["Vu1"][i]:
for Vuj in site_j["Vu1"][i]:
# The Szunyogh-Lichtenstein formula
traced = np.trace(
(Vui @ Gij @ Vuj @ Gji), axis1=1, axis2=2
) # this is the on site projection
# evaluation of the contour integral
storage.append(int_de_ke(traced, cont.we))
# fill up the pairs dictionary with the energies
pairs[tracker]["energies"].append(storage)
# convert to np array
pairs[tracker]["energies"] = np.array(pairs[tracker]["energies"])
# calculate magnetic parameters
for mag_ent in magnetic_entities:
Kxx, Kyy, Kzz, consistency = calculate_anisotropy_tensor(mag_ent)
mag_ent["K"] = np.array([Kxx, Kyy, Kzz]) * sisl.unit_convert("eV", "meV")
mag_ent["K_consistency"] = consistency
for pair in pairs:
J_iso, J_S, D, J = calculate_exchange_tensor(pair)
pair["J_iso"] = J_iso * sisl.unit_convert("eV", "meV")
pair["J_S"] = J_S * sisl.unit_convert("eV", "meV")
pair["D"] = D * sisl.unit_convert("eV", "meV")
pair["J"] = J * sisl.unit_convert("eV", "meV")
times["end_time"] = timer()
print("\n\n\n\n\n")
print(
"##################################################################### GROGU OUTPUT #############################################################################"
)
print_parameters(simulation_parameters)
print_atoms_and_pairs(magnetic_entities, pairs)
print(
"################################################################################################################################################################"
)
print_runtime_information(times)
print("")
# remove unwanted stuff before saving
pairs, magnetic_entities = remove_clutter_for_save(pairs, magnetic_entities)
# create output dictionary with all the relevant data
results = dict(
parameters=simulation_parameters,
magnetic_entities=magnetic_entities,
pairs=pairs,
runtime=times,
)
# save results
save_pickle(simulation_parameters["outfile"], results)
print("\n\n\n\n\n")
if __name__ == "__main__":
main()